Heterodyne Interferometry using
two wavelengths for dimensional measurements
H. J. Tiziani
stuttgart University, Institut of Applied Optics,
Pfaffenwaldring 9, 0-7000 stuttgart 80
1. INTRODUCTION
optical methods become useful tools for dimensional measurements.
Different techniques have been developed in the last few years. In addition to the well known time of flight and phase measuring principles
other methods such as focussing and interferometric techniques are implemented.
Today, laser interferometry is probably one of the most commonly used
interferometric methods in metrology. A stabilized He-Ne laser is fregue9tly used as light source with an absolute stability of better than
10- • The accuracy for length measurements is limited by the atmospheric
conditions (humidity, temperature, pressure) rather than by the laser
stability.
In some applications of interferometry single frequency diode laser
begin to replace the traditional He-Ne laser. Diode lasers are small,
cheap and easy to operate but they lead to some additional requirements.
CUrrent and temperature stabilization is needed for single frequency
operation without mode hops. The spectral emission is very sensitive to
optical feed back (optical isolators are needed). An external reference
is useful for absolute freguency stability. On the other hand their frequency can easily be tuned over tenth of GHz by changing the current and
hunderts of GHz by controlling the temperature.
To measure length with a laser interferometer the fringes are counted
while displacing a mirror respectively a corner cube over the distance.
Any change of the length results in fringe movement followed by forwardbackward counting, as long as no fringes are lost. In this way however,
no absolute distance information can be obtained. In optical profiling
and optical ranging the absolute distance of at least to reference
points is often needed. Furthermore, classical interferometry can only
be applied when smooth surface (optically polished) are to be measured.
Multiple wavelength interferometry allows to reduce the sensitivity
and
2e~end the range of unambiguity for interferometric measurements ' , • The use of multiple wavelengths permits to generate new synthetic wavelengths, which can be much longer than the optical wavelengths used. For two wavelengths Ai and A2 , e.g., one obtains the synthetic wavelength A given by A = '\,'\2/1.\,-.\.1
\0
In order to obtain the desired synthetic wavelengths, single freguency la~ers.at appropriate wavelengths have to be employed. The He-Ne laser w1th 1ts newly available lines in the visible is still a good candidate, but diode lasers have even better potential to cover a wide range
490 / SPIE Vel 1553 Luer Interferometry N : Compurer·AkhId Imerferometry(1991)
O~'9U)681 -3/92/$4.00
of synthetic wavelengths. Absolute distance ranging can be performed by
continuous wavelength tuning, another potential of diode lasers . The
accuracy of multiple wavelength interferometry depends essentially on
the coherence and stability properties of the laser sources.
Multiple wavelength interferometry offers great flexibility in sensitivity by an appropriate choice of the different wavelengths . Two-wav:length heterodyne interferometry was first reported by Fercher et al . •
By simultaneous phase measurement at both wavelengths, the interference
phase at the synthetic wavelength
can be directly determined. This
method provides fast measurements and in addition works for rough
surtaces .
However,
since two wavelengths must be optically seperated
(prism, grating) before detection, the technique can be used only for
relatively large wavelength differences and thus small synthetic wavelength A «1 mm). Because of the availability of tunable diode lasers,
multiple-wavelength interferometry with small wavelength differences is
receiving increased practical interest. TWo wavelength heterodyne interferometry,
sometimes
called two wavelength-superheterodyne
interfero-
metry provides a demodulated signal directly at the synthetic wavelength
and permits therefore high-resolution measurements at arbitrary synthetic wavelengths without the need for interferometric stability at the
optical wavelengths AI and A2 •
2. TWO lIAVELENGTII INTERFEROMETRY
Surface profiling is a useful application of interferometry where the
object beam is focused on an Object that is scanned perpendicularly to
the beam. Height variations 6z present on the surface of the object
will change the phase ~ of the reflected object beam . This phase variation is detected by an interferometer, and measured as a function of
position x on the surface.
A problem, however, occurs if the surface has stepwise height variations greater than A/2 • A discont}nuous height variation 6z introduces a phase jump 641 given by
J ,641 = 4r/A 6z . The interferometer can
only determine the phase cl> modulo 2r •
Furthermore, it would be very useful to apply interferometry to measure optically rough surfaces. An increase of the laser wavelength would
be useful for the metrology of technical surfaces. Laser sources and the
appropriate detectors are frequently not or not yet avalaible. In addition, the high lateral resolution is lost.
In two-wavelength interferometry where the laser emits light with two
slightly different wavelengths AI and A2 , the interferometer detects two
separated interference patterns.
By an appropriate processing of the two individual interference
patterns a new interference term of the form C1JIS(4r/A z) is created where
A ls an equivalent wavelength given by A = AI A2I1AI-A.i
Since the wavelength difference iAI-A.i is usually small, the equivalent wavelength is much larger than the original wavelength used.
Since laser diodes can be easily tuned they are capable of generating a
wide range of equivalent wavelength, making them a good alternative to
more expensive dye lasers or argon lasers.
The two-wavelengths used can either by time mul tiplexed or can be
present continuously. FUrthermore the two-wavel:rngth techniques can be
applied in interferometry as well as holography and Speckle-Interferometry. A typical example of two wavelength interferometry will be given
in fig. 1 for >., -618,6 nm and '\, a550 nm. The object to be tested was
a computer generated reflection hologram with the depth of the grooves
of about 1,6 JIDl
(Fig. 2). Fig. 1 shows the setup for two beam interferometry with phase shifting and two wavelength.
An alternative setup for two-wavelength holography in quasi real time
is shown in fig. 3a, where two holograms are stored in a BSO crystals at
the same time. The two-wavelength '\1' and A'l from an Argon laser are
used. For the reconstruction one-wavelength is selected by fulfilling
the Bragg condition for the BSO-crystal. The reconstructed holograms
lead to contourlines. A typical result of the topographics of a metallic
surface with contour-line seperation of 17 pm •
3. TWO-WAVELENGTH HETEROPYNE INTERFEROMETRY
Two-wavelength heterodyne Interferometry can overcome
some of the
drawbacks ot classical interferometry. A scanning two wavelength speikle
interferometer using a Krypton laser was described by Fercher et al . .
In a heterodyne interferometric set-up two waves are superposed to
lead to an interference phenomenon. One of the two beams is frequency
shiftened by f.
The optical heterodyne signal is
I = I,
+ I. + 2!I.1. 006{27fft +~)
The detected heterodyne signal is arranged to be shot noise limited.
There are different techniques to introduce the frequency shift such as
using an acousto optical modulator (AOH) or a rotating grating or by
using the Zeeman splitting in a laser cavity.
In the oHI (double heterodyne interferometry) two heterodyne interference systems are superimposed to lead to a beat trequency ot the two
wavelength responsable for the distance measurement.
The heterodyne signals
Ih(t) are
Ih(t) = 2/ I" 1&1 006{27ff,t +~) + 2/ I .. I.. 006{27ff, t + M
Ir1 ' ISl ' IS2 , IS2 are the intensities of the interfering reference
and signal beams for the two wavelengths, fl and f2 are the heterodyne
frequencies
47f
['"
~=-z-27f
'\,
+
c
filL
4 .. -2.. ["" +
4>.l = -z
~2
f2] L
C
z is the object distance to be measured and c the velositiy of the light
III ,
J"J
are the frequencies of the corresponding wavelength
~2
.xl
and
, L is the reference path. The heterodyne signal after the mixer is
Ish(t) (superheterodyne signal)
where
In double heterodyne interferometry two laser wavelengths and two
heterodyne frequencies are used simultaneously. A low frequency detec-
tion signal with a phase shift that corresponds to the effective wavelenqth is qenerated. A two-wavelength double heterodyne interferometer
(DHI) setup consists basically of two independent heterodyne interferometers working at different wavelengths
~1
and ~2
and different
heterodyne frequencies £1 and £2 . The phase of the beat frequency f 1 -f 2
depends on the effective wavelength A and can th;r~fore be examined for
distance evaluation as shown by Dandliker et al. ' • Using two (highly
stable)
laser sources emitting different wavelengths,
the heterodyne
frequency shifts can easily be obtained by acoustooptical modulation
(ADM) as shown in Fig. 4. The unshifted wavelengths are combined in a
beam splitter (BS) and a monomode fiber (MMF) to generate an identical
wavefront before being focused onto an optically rough specimen.
Only identical wave fronts of
~1
and
~2
will generate identical spec-
kles in the entrance pupil of the imaginq system and onto the detector.
After passing a lens (L), a polarizing beam splitter (PBS) and a
quarterwave plate the light is focused onto the specimen by a microscope
objective (MO) as shown in Fig. 4. The quarterwave plate is passed twice
and used to rotate the polarization by 90 0 to achieve reflection at the
polarizing beam splitter. To match the polariziations of the reference
and the tarqet beam the polarization in the tarqet beam is then rotated
back by a halfwave plate (HWP) and combined in a beam splitter with the
heterodyne frequency shifted beams~ The interference signal is observed
by a photodetector (Det). The beat frequency is generated by squaring
the signals with a Schottky diode and then fed to a phase detector. The
reference siqnal for the phase detector is generated in an additional
interference arrangement to compensate for phase fluctuations of the two
highly stable laser sources.
In the case of a multiline laser,
to be discussed
~ere,
the wave-
SPIE VoL '553 hSllf Inf"rf"fotrltltr'( N: Comput"r..4idtJdlnf"rf"romtlfry{1"'J / 4S3
lengths Al and.\2 are perfectly combined and have a good relative stability. In a conventional setup (similar to the one shown in Fig. 4),
but with a multiline laser instead of two lasers) the laser radiation
would be first divided into target and reference beams.
The OH! is very appropriate for high precision absolute measurements.
For the realization of a OHI there are different possibilities . At first
two diode laser to give AI and A. look very promising. An interesting
way to obtain the various wavelength is to use a single laser diode in
combination with a Bragg cell and two acousto optic modulators (AOM's).
The high frequency AOM to be driven by 500 MRz and 501,5 MRz leading to
wavelengths of 60 cm and 200 m (for 1,5 MHz). An experimentel setup is
shown in fig.5. The two AOM's driven at 80 and 80,1 MRz lead to the frequency difference of f 1-f 2 100 kMz. Fluctuations of the AOM frequencies
fl and f2 will affect thelCeat detection frequency f 1-f 2 but not disturb
the phase measurement if the reference signal for the phasemetar is
interferometrically generated. In fig.6 it should be indicated that the
object can be scanned with the koaxial focused beams with
Al
and
A. produced by the high frequency AOM. For synthetic wavelengths of
200 m and 60 cm absolute measures up to 100 m with a resolution of 0,1
g
mm can be obtained. It should however be noted that almost focussed coaxial laser beams are needed. FUrthermore only a few speckles should be
accepted by the aperture respectively the detector.
4. POUBLE HETERODYNE INTERFEROMETER WITH ROTATIONAL MATCHEP GRATING
A two-wavelength heterodyne interferometry technique vas developed
tor precision measurement. The heterodyne frequency difference for the
two wavelength was generated by a rotating grating for instance.
After
passing a lens L , a polarizing beam splltter PBS
and a quarter wave
plate (QWP) the object beams are focussed on to the specimen under test
by a microscopic objective (MO).
In the set-up shown in fig. 6 the AOM is operated at driver frequency
fd leading to two frequencies in the first order diffracted beam for
AI of lit ... f d and for A. of "l + f d • AI and A. are the wavelengths
and lit ,"l
the frequencies of the two wavelengths, fd is the shifted
frequency, strlfted by the AOM.
The beams pass two diffraction gratings. The diffraction at the first
grating (G) with a high spatial frequency (600 lp/mm) splits the two
HeNe frequencies ~ and ~ where the first diffraction orders occur at
a.. and U'J • The grating was designed in such a way (and produced on
photoresist) that the diffraction angle difference ~a
between lit +fd
and "l +fd is compensated at a second (lOW spatial frequency) grating.
Therefore ehe first order diffraction of '1 +fd and the zero order of
~ +t d , as well as the zero order of Vi +f
d and the minus first order
of
"l+fd , become parallel as shown in fig. 6.
The second grating (RG) is a standard low cost angle encoder (Hewlett
Packard) with a spatial frequency of about 7.2 lp/mm. It is continuously
rotated by a motor. Due to a rotation of the grating, the first order
diffracted light is frequency shifted by f while the zero order light
passes the grating unaffected. Selecting on~ pair of parallel beams (as
,f9f
I SPIE VoL 1663 t..ar/",."eromwylV: COl'fPUUI-Aidttdlntert.ram.try(1991)
shown in fig. 6) the frequencies of the beams are written as
~
/I,
+f l and
+f2 where f1-fd+f m and f2~fd· They serve as reference beam in the
interferometer. The beat frequency f m=f l -f 2 is generated due to the ro-
tation of the angle encoder. In the exper1ment the angle encoder wheel
with 1000 lp/revolution and was rotated with 1200 revolutions/minute,
the heterodyne beat frequency of 20 KHz was found to be most appropriate. This frequency can be directly applied to a low frequency phase
meter (e.g. two channel lock-in-amplifier LIA).
The reference for the lock-in-amplifier is directly taken from the
angle encoder detector (square wave signal) output. Care must however be
taken by the design of the encoder wheel when phase fluctuations
1n the reference path occur. The beat of the two heterodyne signals can
be observed after demodulation and bandpaB filtering, leading to
U(I) = UD ros(2.. f. I -4 ../A z + 'P). Results were otained with a 10x microscope
object1ve and an avaLanche diode as photodetector. The diffraction limited target spot was in the order of 3 ~ . The clear working distance to
the target was 6.5 mm.
The target was moved with a computer controlled stepper motor. Figure
7 shows a measurement where the target distance was varied by 100
~
.
The unambiguous distance range of 27.7 ~ as well as the good linearity
can be observed when a mirror like structure was displaced.
Two successive measurements on a machined aluminium sample are shown
in fig. 8. On the sample two steps of 5
~
and 10
~
were milled into
the surface. In the experimental set-up a resolution in the order of
0.5 pm was obtained. It is expected to improve the resolution by the
use of a solid state approach to be reported later.
Two wavelenqth double heterodyne interferometry has proven to be a
powerful tool for accurate interferometric measurements on smooth as
well as on optically rough surfaces. It is important especially for
rough target surfaces that the system behaves like a heterodyne inter-
ferometer with a synthetic wavelength A = >., >'2/1>.,->'21 • In the special
arrangement the effective wavelength was 55.5 pm. The laser wavelength
itself were (632.8 nm and 640.1 nm).
Due to intensity fluctuations an automatic gain control should be
foreseen especially when an avalanche diode is used as photodetector.
Intensity thresholding to reject distance data in case of low amplitudes
was not required in our experiments.
The matched grating principle was extended and modified and the moving grating was replaced.
5. DOUBLE HETERODYNE INTERFEROMETER WITH SOLID STATE HATCHED GBATINGS
Figure 9 shows a mul tiwavelength He-Ne laser
( (Spindler
&
Hoyer)
tuned to emit simultaneously and with equal intensity at 632,8 run and
640.1 nm. This leads to an effective wavelength of 55.5 ~ • As shown,
only one AO" is required (compared to the setup shown in F1g.4). The AO"
is operated in suppressed carrier mode, where a modulation signal fm is
applied to the AOM driver, while the driver carrier amplitude is turned
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'653 LeUf lnrerferom~tr( N: Computer-Aided InterfefOl'Mrry(199' JI
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to zero. This results in a multiplication of the driver carrier frequency f
with the modulation frequency fm leading to two side bands
f =fd~f and f2=fd-fm and suppressed carrier fd' As a result, the AOM is
o~erate~ at two frequencies, fL and f2' simultaneously. Two individual
phase gratings are established in the AOM crystal leading to two firstorder beams that leave the AOM under slightly different angles ot and
/lO)
• The diffraction efficiency (the enerqy distribution between the
zero-order and the two first-orders) is optimized (bragg angle) and
adjusted with the driving power of the modulation signal f m. In this way
the frequencies of the two first-order diffracted beams are '" +fd-t.. ,
... +fd-fm and &It +fd+fm, ... +fd+fm respectively.
The small angle between the two first-order diffracted beams is
approximately given by
~
Aa=2-f.
"
where .\ - .\, or ~. one of the He-Ne laser wavelengths (the spatial frequency of the AOM phase grating is far too low to seperate the two laser
wavelenqths .\, and'\.
The term " is the speed of sound in the AOM
crystal.
In our new approach, we matched the anqle
the first-order diffraction angle (between A,
using a high spatial frequency grating (G).
Aa to the difference of
and A. ) was matched by
with the spatial frequency '1 of the grating. Matching two gratings accordingly, only beams with frequencies &It +fd-fm and ... +fd+f become
parallel. They are extracted to serve as reference for the in'terferometer as shown in Fig.9. In this setup there is no (or hardly any) reference pathlenqth difference introduced as compared to the setup shown
in Fig. 4 • This makes the system almost insensi tive to laser frequency
variations. The shear of the reference beams shown in Fig.9 is negligible because of a very small divergence angle Aa • The modulation frequency is generated by an oscillator and divided by two before being
applied to the AOM driver. Because of the two sidebands generated, the
beat frequency is twice that of the modulation frequency f m• Further
down-mixing of the signals is helpful, since highly accurate phase
meters are easier to obtain that work at low frequencies.
6. CONCLI1SION
Heterodyn interferometry is a powerful tool for high precision distance and vibration
analysis. Two wavelength heterodyne techniques
become very interesting for absolute distance measurement. It was shown,
that a synthetic wavelength can be generated by two shorter ones. This
leads also to the techniques to measure optically rougher surfaces
because the optical path difference is to be compared with the synthetic
wavelenqth. Further work will be reported.
496 I SPlE Vol. '663 LIar InYrf_tOnNlrt IV: Comput.r-.4ided InteriMNNtJy,' 99'J
7. ACKNOWLEDGEMENT
I thank for the contribution and discussion with Z.Sodnik, E.Fischer
and Th.Ittner from the Institute of Applied optics, S.Manhart and
R.Maurer from Messerschmitt-Bolkow-Blohm, as well as P.Rou8sel from the
EUropean Space Research and Technology Center.
8. REFERENCES
1. J.c.Wyant, "Testing Aspherics Using Two Wavelength Holography,"
Appl. opt. 10, 2113-18(1971)
2.
F.M.Kuchel,
and
H.J.Tiziani,
"Real-Time contour Holography
Using BSO Crystals, "Opt. Commun. 38, 17-00(1981).
3. ·C.Polhemus."Two-Wavelength Interferometry,"Appl.Opt.12,20712074(1973).
4. A.F.Fercher,H.z.Hu.and U.Vry"Rough Surface Interferometry with
a Two-Wavelength Heterodyne Speckle Interferometer,"Appl.Opt.
24,2181-2288(1985).
5. R.Dandllker,R.Thalmann, and D.Prongue, "Two Wavelength Laser
Interferometry Using Super-Heterodyne Detection,ItProc.Soc.Photo-Opt.
Instrum.Eng.813(1987).
6. Z.Sodnik,
E.Fischer,
I. Ittner, H.J.Tiziani,
"Two wavelength
double heterodyne Interferometry using a mathed grating
technique, Appl.Opt.(in print).
beQm
spI.ller
reference
Fiqure 1. Linnik Interference microscope arrallqement.
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1.6 pm
•
l'-V : 1.591,at
··ol-!:!.-'~-"'--="-::I:!:OO;:::'--'::::'-':::"'-=';:I" ...
•
ICM lctII'h
time
Figure 2. Topography of a reflection grating obtained by
plexed two-wavelength interferometry with
.)
multi-
b)
,
"
•
Figure 3. a) setup for guasi real time two wavelength holography using a
BSO crystal as storage material.
b) A reconstructed object, a metallic surface, with the contour-line separation of 17 JlID.
498 I SPIE VoL 1553 Luer Interferometry 11/.. COf'I'IP(Ifer-AK»d Interferometry, 199 1I
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:~Io:s:er::;;.~
z
loser
"2
PBS
111111111
f
AOM
AOM 2
i ( t)
Figure 4. Principle of two-wavelength double heterodyne interferometry.
AOM
I,al.tor
UHF·AOM
=
/
L".r
0.
0,
0.
Figure 5. Possible realisation of two-wavelength double heterodyne interferometry using a UHF AOM.
SPIE Vol. '553 t.., InttlfferrJItNtty IV: Comput"r-Aided Inrtlrferomatry{IGG'J / 499
L
PBS awp
,,
,,
MO
•• ••
"
AOM·Orlw.r
000
2'.
2'.
Figure 6. Principle of OHI with
rotationed matched
grating
I
I
,.
.
. .--. . . . ... -.-
.-.L-~-.c-;-~-.~=--.-.;~ "
"
Figure 7 • Phase response from a
target distance variation of 100 pm
...
•••
•••
.
....
T .•.•
t ....
1 ....
.....iA
..•
.u .• l1vv\,J
~
-\
. '--;:;---;:;--.:;--.~-;;:;-.
f
• ••
_ of
• ••
• ••
,. . .
.. ••
- -
Figure 8. Result of two successive
line focus on a milled
aluminum sample with
step heights of 5 JJfI1
and 10 JJfI1
IIWP ,.£!_
LnSER
\
v.,'i
--
-----
/
/
IioH
PST VWP L2
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"
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r.
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r..
[pHAsE METER
n
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~
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Figure 9. Principle of OHI solide state matched grating.
SPIE Vol. '553 bSl8r In/tuf.rometry IV: Comput6r-Aided Int~rflJrometly(199'J I 501